Question

A document showed that the settlers of Plymouth were ready to govern themselves it showed that they agreed to live together according to a systems of laws what was it

Answer 1

This is it:

It was the Mayflower Compact.

This is why:

I would explain what the Mayflower Compact is, but the question already does that.

However, a little extra piece of information on the document can be assumed. The ship that took the same settlers of this question to Plymouth was called the Mayflower. It can be assumed that they named the Mayflower Compact after their ship, and simply added compact as a word to describe their treaty (since one of compact's definition as a noun is a formal agreement, similar to this document).

^ Technically this is totally unnecessary, but perhaps it will do a bit in convincing you of my accuracy. :)

If it's still confusing, then here; take a snippet from an official history book that contains the information thou likely seeks:

Answer 2

Which document showed that the settlers of Plymouth were ready to govern themselves that they agreed to live together according to a system of laws?

The Mayflower Compact created laws for Mayflower Pilgrims and non-Pilgrims alike for the good of their new colony. It was a short document which established that: the colonists would remain loyal subjects to King James, despite their need for self-governance.

Step-by-step explanation: